Hitchin [1]} and Tod [2]} realized that (anti-)self-duality in Bianchi IX metric has a more general solution envolving to a Darboux–Halphen system coupled to another system of linear differential equation similar to Darboux–Halphen. A revised and simplified proof of the results of Tod and Hitchin can be found in [3]}. See [4]} for a physical application in cosmology. We review these works in Section .
